If a Runner runs on a server with one piece of ICE and a single card installed in the root, proceeds past the ICE (either by breaking it or by it not being rezzed - I don't think it matters), but then the card in the root is removed or trashed (let's say it's a Jackson for example), does that count as a successful run for the purpose of card abilities which are dependent on the Runner having made a successful or unsuccessful run the previous turn?
Does the answer change if there is no ICE on the server and so when the card in the root is removed, the server ceases to exist?